College of the Holy Cross, Fall 2017

Syllabus for Math 302 (Differential Geometry)

Professor Hwang, (rhymes with song)

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Do not make travel plans that conflict with the midterm tests or your final exam. If an emergency prevents you from taking the final exam at the allotted time, speak to your Class Dean immediately to arrange for an incomplete grade, and to me to schedule a make-up exam.

The schedule below is subject to minor changes. Any substantial corrections will be announced by email and/or in class.

Day Date Section Topics
M Aug 28   Advising
W Aug 30 Section 1.1-1.2 Curves, Arc Length
F Sep 1 Section 1.3 Reparametrization
M Sep 4 Section 2.1 Curvature
W Sep 6 Section 2.2 Plane Curves
F Sep 8 Section 2.3 Space Curves
M Sep 11 Section 2.3 The Frenet Formulas
W Sep 13 Section 4.1 Surfaces
F Sep 15 Section 4.2 Smooth Surfaces
M Sep 18 Section 4.3 Smooth Maps
W Sep 20 Section 4.4 Tangents and Derivatives
F Sep 22 Section 4.5 Normals and Orientability
M Sep 25 Section 5.1 Level Surfaces
W Sep 27 Section 5.2 Quadric Surfaces
F Sep 29 Section 5.3 Ruled Surfaces, Surfaces of Rotation
M Oct 2 Section 5.3 Ruled Surfaces, Surfaces of Rotation
W Oct 4 Section 5.4 Polyhedra
F Oct 6   Midterm 1
M Oct 9   Fall Break
W Oct 11   Fall Break
F Oct 13   Fall Break
M Oct 16 Section 5.4 Compact Surfaces
W Oct 18 Section 6.1 The First Fundamental Form
F Oct 20 Section 6.1 The First Fundamental Form
M Oct 23 Section 6.2 Isometries
W Oct 25 Section 6.3 Conformal Mappings
F Oct 27 Section 6.4 Equal-area Maps
M Oct 30 Section 6.5 Spherical Geometry
W Nov 1 Section 6.5 Spherical Geometry
F Nov 3 Section 7.1 The Second Fundamental Form
M Nov 6 Section 7.2 The Gauss and Weingarten Maps
W Nov 8 Section 7.3 Normal and Geodesic Curvatures
F Nov 10 Section 7.4 Covariant Derivatives
M Nov 13 Section 7.4 Parallel Transport
W Nov 15 Section 8.1 Gaussian Curvature
F Nov 17 Section 8.1 Gaussian and Mean Curvature
M Nov 20   Midterm 2
W Nov 22   Thanksgiving
F Nov 24   Thanksgiving
M Nov 27 Section 8.2 Principal Curvatures
W Nov 29 Section 8.3 Surfaces of Constant Curvature
F Dec 1 Section 8.3 Surfaces of Constant Curvature
M Dec 4 Section 9.1 Geodesics
W Dec 6 Section 13.1 The Gauss-Bonnet Theorem
F Dec 8 Section 13.1 The Gauss-Bonnet Theorem